Trigonometric Equations Quiz

What is the interval over which we solve trigonometric equations analytically in this tutorial?

• 0 to π

• 0 to 4π

• 0 to 2π

• 0 to π/2

For the equation cosine of 2x equals negative one-half, what is the adjusted domain for 2x?

• 0 to π

• 0 to 2π

• 0 to 4π

• 0 to 3π

How many solutions are there for the equation cosine of 2x equals negative one-half within the interval 0 to 2π?

• 2

• 5

• 3

• 4

What is the domain for x/2 when solving the equation sine of x/2 equals one-half?

• 0 to 3π

• 0 to π/2

• 0 to 2π

• 0 to π

What are the solutions for x in the equation sine of x/2 equals one-half?

• π/4 and 3π/4

• π/6 and 5π/6

• π/2 and 3π/2

• π/3 and 5π/3

Which trigonometric identity is used to rewrite cosine of 2 theta in terms of sine?

• cos(2θ) = 1 - 2sin²θ

• cos(2θ) = 1 + 2sin²θ

• cos(2θ) = 2cos²θ - 1

• cos(2θ) = cos²θ - sin²θ

What type of equation does the identity transform the problem into when solving sine of theta equals cosine of 2 theta?

• Cubic equation

• Quadratic equation

• Linear equation

• Exponential equation

What are the solutions for theta when sine of theta equals negative one?

• 2π

• π

• 3π/2

• π/2

Why are trigonometric identities useful in solving equations?

• They increase complexity

• They change the domain

• They eliminate variables

• They simplify equations

What is a key consideration when solving trigonometric equations involving double or half angles?

• Avoiding identities

• Ignoring the domain

• Adjusting the domain

• Using only sine functions